arXiv subjects
Publications and source records attributed to Vittorio Cafagna.
In this article we explore some aspects of Fourier analysis on fuzzy sets. This work was part of a broader project jointly with Professor Vittorio Cafagna which spanned over a few years between 1998 and 2005. Professor Cafagna passed away unexpectedly in 2007. His intellectual breadth and inspiring passion for mathematics is still very well alive today.
We propose in this article a definition of a MV-algebra structure on a class of subsets of some probability spaces and we work-out some examples. Our intention is to convey, by mean of the simplest possible examples, the idea that the topology of the geometric object under consideration might be reflected in the MV-algebraic structure. We also discuss an example of Chang and discuss similarities and differences with the proposed class of examples.
In these notes we propose a setting for fuzzy computing in a framework similar to that of well-established theories of computation: boolean, and quantum computing. Our efforts have been directed towards stressing the formal similarities: there is a common pattern underlying these three theories. We tried to conform our approach, as much as possible, to this pattern. This work was part of a project jointly with Professor Vittorio Cafagna. Professor Cafagna passed away unexpectedly in 2007. His intellectual breadth and inspiring passion for mathematics is still very well alive.